✦ LIBER ✦

Integrating Unitary Representations of Infinite-Dimensional Lie Groups

✍ Scribed by Valerio Toledano Laredo

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 237 KB
Volume: 161
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3359

No coin nor oath required. For personal study only.

✦ Synopsis

We show that in the presence of suitable commutator estimates, a projective unitary representation of the Lie algebra of a connected and simply connected Lie group G exponentiates to G. Our proof does not assume G to be finite-dimensional or of Banach Lie type and therefore encompasses the diffeomorphism groups of compact manifolds. We obtain as corollaries short proofs of Goodman and Wallach's results on the integration of positive energy representations of loop groups and Diff(S 1 ) and of Nelson's criterion for the exponentiation of unitary representations of finite-dimensional Lie algebras.

📜 SIMILAR VOLUMES

Low-Dimensional Representations of Speci

Low-Dimensional Representations of Special Unitary Groups

✍ Gerhard Hiss; Gunter Malle 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 170 KB

We prove gap results for the low-dimensional representation of unitary groups in nondefining characteristics. More precisely, we give a lower bound for the third smallest degree of a nontrivial absolutely irreducible representation of the groups mentioned above, which is almost in the order of magni

Restrictions of Irreducible Unitary Repr

Restrictions of Irreducible Unitary Representations of Nilpotent Lie Groups to Lattices

✍ M.B. Bekka; P. Driutti 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 172 KB

## RESTRICTION OF REPRESENTATIONS with Q-linearly independent real numbers : 1 , : 2 . Then By Proposition 1.1, r l is not contained in a proper rational ideal of g. So, ? l | 1 is irreducible, by Theorem 1.1. Now, if f =n 4 X 4 \*+n 5 X 5 \* # g\* with n 4 , n 5 # Z&[0] then it is easy to see th

Weil Representations of Unitary Groups

✍ Fernando Szechtman 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 207 KB

Digraphical Regular Representations of I

Digraphical Regular Representations of Infinite Finitely Generated Groups

✍ R.G. Möller; N. Seifter 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 104 KB

A directed Cayley graph X is called a digraphical regular representation (DRR) of a group G if the automorphism group of X acts regularly on X . Let S be a finite generating set of the infinite cyclic group Z. We show that a directed Cayley graph X (Z, S) is a DRR of Z if and only if As a general r

Isomorphisms of Integral Group Rings of

Isomorphisms of Integral Group Rings of Infinite Groups

✍ E. Jespers; S.O. Juriaans 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 138 KB

This paper deals with the isomorphism problem for integral group rings of infinite groups. In the first part we answer a question of Mazur by giving conditions for the isomorphism problem to be true for integral group rings of groups that are a direct product of a finite group and a finitely generat

Some Characterizations of the Weil Repre

Some Characterizations of the Weil Representations of the Symplectic and Unitary Groups

✍ Pham Huu Tiep; Alexander E. Zalesskii 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 425 KB

Let G be a finite symplectic or unitary group. We characterize the Weil representations of G via their restriction to a standard subgroup. Then we complete the determination of complex representations of G with specific minimal polynomials of certain elements by showing that they coincide with the W